Side-mode suppression mechanism of gain-coupled DFB lasers with periodically etched quantum wells

The effect of the gain and index coupling on the side-mode suppression ratio (SMSR) is studied for gain-coupled DFB lasers with periodically etched quantum wells. An accurate expression for the SMSR based on the amplified spontaneous emission model is used with the local-normal-mode transfer-matrix method. The mechanism for the strong single-mode stability of the gain-coupled DFB lasers is explained by the difference between the effective gain and loss of the Bloch waves in the grating structures. This new view clearly shows the advantage of the gain-coupled DFB lasers in terms of single-mode stability.     

Basic analysis of AR-coated, partly gain-coupled DFB lasers: thestanding wave effect

A theoretical analysis of distributed feedback (DFB) lasers with mixed gain and index coupling (partly gain-coupled DFB) is given for perfect antireflection (AR) coatings. Analytical expressions for the threshold gain, facet loss, and the relative depth of the standing wave pattern are derived. At the same time the importance of the standing wave effect and its consideration by coupled mode equations is shown. For purely gain-coupled DFB lasers, simple expressions for the effective linewidth enhancement factor and the longitudinal spontaneous emission factor are derived. In addition, various approximations describing the performance of purely gain-coupled DFB lasers are given     

Transfer-matrix dynamic model of partly gain-coupled 1.55 μm DFBlasers with a strained-layer MQW active grating

A dynamic model for partly gain-coupled 1.55 μm MQW DFB lasers consisting of etched strained-layer multiquantum wells is presented. For the modulation and noise characteristics of DFB lasers, analytical expressions which take into account both the longitudinal distribution of laser parameters and carrier transport effects are derived for the first time using the transfer-matrix method. As a numerical example, the relaxation oscillation frequency is compared to experimental results, and reasonable agreements are obtained between the theory and experiment     

Transient side-mode suppression in gain-coupled DFB lasers

Based on the spatially dependent multimode rate equations, we investigate the transient side-mode suppression in the gain-coupled distributed feedback (DFB) lasers. A simplified but accurate multimode dynamic analysis of gain-coupled DFB lasers is developed. To first order of perturbation approximation, the study includes various spatial effects, such as the distributed complex coupling, the nonuniform carrier distribution, and the nonlinear gain compression. It is found that gain coupling introduces high decay rates and low dynamic differential gains for the side modes, which effectively suppress their transient fluctuation and shorten the rise time of the transient side-mode suppression ratio (SMSR)     

Self-consistent analysis of side-mode suppression in gain-coupledDFB semiconductor lasers

Based on a set of spatially dependent multimode rate equations derived from Maxwell's equations, a self-consistent analysis of gain-coupled distributed feedback (DFB) lasers is developed. By introducing the modal net gain into the coupled wave equations, we also obtain a closed form formula of the side-mode suppression ratio (SMSR) for DFB lasers. It is shown that, associated with the distributed feedback, the longitudinal spatial hole burning, and the nonlinear gain compression effects, gain coupling produces significant effects on the SMSR of DFB lasers     

Improvement of single-mode gain margin in gain-coupled DFB lasers

Using the Bloch-wave analysis, this paper investigates the effect of the gain grating on the single-mode condition in DFB lasers. Various factors affecting the threshold gain of gain-coupled DFB lasers are analyzed in some detail. It is shown for the first time that unequal section lengths in the gain grating can have a significant effect on the single-mode gain margin of gain-coupled DFB lasers, especially when the linewidth enhancement factor α_M is large, because the long and shortwavelength Bloch waves are in phase and in antiphase with the index grating of DFB lasers, respectively     

Distributed feedback lasers in chiral media

The combined effects of chirality and gain (or loss) on wave propagation and coupling in periodic structures is investigated here. The focus is on distributed feedback (DFB) lasers in a transversely unbounded periodic slab with spatially modulated electromagnetic parameters. The analysis uses a coupled-mode approach employing a canonical physical model of chiral materials to predict the effects of modulated chirality admittance on DFB lasers. Results for DFB laser behavior in chiral media are compared and contrasted to that in achiral media. It is found that, under certain circumstances, the electric and magnetic field coupling, which is characteristic of chiral materials, results in a lower threshold gain for DFB lasers in media with a given index of refraction and characteristic impedance. It is also found that chiral index-coupled or gain-coupled DFB lasers exhibit the same spectral mode properties as achiral DFB lasers     

Enhanced maximum intrinsic modulation bandwidth of complex-coupled DFB semiconductor lasers

DFB lasers with complex (gain and index) coupling are shown to have reduced K-factors, that is increased maximum intrinsic modulation bandwidths, compared with pure gain-coupled lasers. The K-factor is shown to be dependent on the ratio and phase of the index coupling to the gain coupling. Appropriate choice of the ratio of index coupling to gain coupling can triple the maximum intrinsic modulation bandwidth of the laser.<>     

Effects of structural parameters on the external optical feedbacksensitivity in DFB semiconductor lasers

External optical feedback sensitivity in distributed feedback (DFB) semiconductor lasers is analyzed with special attention to phase-shifted and complex-coupled lasers. The effects of various structural parameters such as coupling strength, facet reflectivity, and corrugation phase angle on external optical feedback sensitivity are studied. The λ/4 phase-shifted index-coupled DFB laser exhibits low external optical feedback sensitivity for large index-coupling coefficient and high facet reflectivity. Pure gain-coupled DFB lasers perform better than the phase-shiftless uniform index-coupled DFB lasers but worse than λ/4 phase-shifted index-coupled lasers with high coupling strengths. External optical feedback sensitivity of complex-coupled lasers depends significantly on the index-to-gain coupling ratio, the phase between the index and gain gratings, and the total coupling     

Gain-coupled DFB lasers versus index-coupled and phase shifted DFBlasers: a comparison based on spatial hole burning corrected yield

A statistical yield analysis is presented for gain- and index-coupled distributed feedback (DFB) laser structures, allowing a comparison of their single longitudinal mode (SLM) yield capabilities. For the yield calculations, the threshold gain difference and the longitudinal spatial hole burning (SHB) are taken into account. By comparing the experimental and theoretical yield of index-coupled DFB lasers, the significance of SHB for correct yield predictions is illustrated. For the purpose of comparison, yield calculations for various λ/4-shifted DFB lasers (with low facet reflectivities) are presented. The most emphasis, however, is on partly gain-coupled DFB lasers. Estimations of practical gain coupling coefficient values for gain and for loss gratings are discussed     

Self-suppression effect of longitudinal spatial hole burning inabsorptive-grating gain-coupled DFB lasers

Longitudinal spatial hole burning (LSHB) induces degradation of longitudinal-mode stability in distributed-feedback (DFB) lasers. Measurement of frequency modulation characteristics has revealed that, in absorptive-grating gain-coupled DFB lasers, the LSHB diminishes as power increases. This anomalous behavior has been qualitatively explained by a theoretical analysis that took into account the saturable nature of the absorption of the gain-coupled grating. This LSHB suppression effect is advantageous for high-power single-longitudinal-mode operation of DFB lasers     

External feedback sensitivity of partly gain-coupled DFBsemiconductor lasers

External optical feedback sensitivity of partly gain-coupled DFB semiconductor lasers has been analyzed in above threshold operation regime. Both the longitudinal spatial hole burning and the nonlinear gain compression have been taken into account. A comparison has been made among λ/4-shifted, pure index-coupled and partly gain-coupled DFB laser diodes. Even though pure index-coupled and partly gain coupled DFB lasers exhibit similar sensitivity to external optical feedback at the threshold, however, gain grating can reduce the feedback sensitivity when the lasers operate well above the threshold specially when the κL parameter is high     

Theoretical investigation of the second-order harmonic distortionin the AM response of 1.55 μm F-P and DFB lasers

Numerical calculations of the second-order harmonic distortion in the amplitude modulation-response of Fabry-Perot, and distributed feedback (DFB) lasers are presented, and the influence of several nonlinearities, such as longitudinal spatial hole burning, gain suppression, and relaxation oscillations are considered. This analysis is valid for modulation frequencies ranging from a few megahertz to well beyond the resonance frequency of the relaxation oscillation. The distortion of Fabry-Perot lasers for which the effects of spontaneous emission and gain suppression can be clearly illustrated is investigated. The distortion of DFB lasers where the emphasis is on the influence of spatial hole burning and its combination with other nonlinearities is discussed. Various effects are discussed     

Optimization of grating duty factor in gain-coupled DFB lasers withabsorptive grating-analysis and fabrication

Grating duty factor strongly affects the performance of gain-coupled (GC) distributed feedback (DFB) laser diodes with an absorptive grating. Through numerical analysis the authors have found an optimum value in the duty factor for their low threshold operation. The minimum threshold gain achievable at this optimum duty factor is found to be almost independent of the order of the grating. According to this prediction, the authors have fabricated GaAlAs/GaAs GC DFB lasers with a third-order absorptive grating where the grating duty factor has been made close to the theoretical optimum value. In 200-μm-long devices with both facets as-cleaved, low CW threshold current of 25 mA, external efficiency of 0.5 mW/mA, and SMSR as high as 45 dB have been obtained, which is qualitatively consistent with the analysis. High yield of single mode oscillation seems to be the result of the gain coupling     

Effect of in-phase and antiphase gain coupling on high-speedproperties of MQW DFB lasers

Effect of in-phase and antiphase gain-coupling on high-speed properties is studied for MQW DFB lasers with periodically truncated quantum-wells. The enhancement of modulation bandwidth due to antiphase gain-coupling is found significantly suppressed, and gain-coupled DFB lasers with high κL are preferred for large modulation bandwidth due to the presence of linear gain saturation in MQW lasers     

Extraction of gain parameters for truncated-well gain-coupled DFBlasers

An amplified spontaneous emission transfer matrix model for prediction of the subthreshold spectral output of distributed-feedback (DFB) lasers was developed and fitted to the spectra of truncated-well gain-coupled DFB lasers using a least-squares-fitting algorithm. Modal gains for the high- and low-gain segments of the truncated-well DFB lasers were extracted, and their evolution as a function of injection current was examined. Results explain the tendency for the truncated-well gain coupled DFB lasers to have higher yields of single-frequency lasers and larger sidemode suppression ratios than are expected from simple considerations     

The symmetry of the amplified spontaneous emission spectrum incomplex-coupled DFB lasers

We present relations between facet reflections and coupling coefficient for the amplified spontaneous emission (ASE) spectrum of a complex-coupled, an index-coupled, and a gain-coupled distributed feedback (DFB) laser to have a mirror image with respect to the Bragg wavelength. We show that the ASE spectrum of a complex-coupled DFB laser cannot be symmetric in general with respect to the Bragg wavelength. The index-coupled and gain-coupled DFB lasers can have symmetric ASE spectrum for some values of the phase of the facet reflection coefficient that are determined     

Performance comparison of gain-coupled and index-coupled DFBsemiconductor lasers

Comprehensive numerical simulations with the transmission-line laser model (TLLM) are used to compare the behavior of gain-coupled DFB lasers with index-coupled DFB lasers fabricated from identical materials. These simulations compare slope efficiency, threshold current, spectra, small-signal modulation bandwidth, maximum-intrinsic modulation bandwidth, large-signal transient response and chirp, relative-intensity-noise (RIN) spectra, and feedback sensitivity for coherence collapse. In most cases gain-coupled lasers with additional index coupling have better performance than index-coupled lasers for a given material. However, high-coupling factor index-coupled lasers do have lower threshold currents, lower RIN levels, and lower sensitivity to external feedback than gain-coupled lasers, although spatial hole burning in these devices can be disadvantageous     

Fluctuations of the laser characteristics and the effect of theindex-coupling component in the gain-coupled DFB laser

The normalized oscillation frequency δL and threshold gain αL of gain-coupled distributed feedback (DFB) lasers with an AR/AR (symmetric) structure vary significantly with a variation in the corrugation phase at the facets when the facet reflectivity |r| is large, even though the spatial-hole-burning-corrected yield is 100%. For example, the standard deviation for the δL, σ(δL), increases from 0.018 to 0.40 when |r| is increased from 0.03 to 0.30. The magnitude of σ(δL) and σ(αL) are small, however, for the gain-coupled, index-coupled, and complex-coupled DFB lasers when the |r| is kept small. For the HR/AR (asymmetric) structure, these two values are more than an order of magnitude larger than those for the AR/AR structure, except for the σ(αL) for the index-coupled laser, even though yields of each of these lasers are relatively large. In the AR/AR structure, the contamination by the index-coupling and gain-coupling components always degrades the device characteristics because of the difference in the phase shifter and when the amount of contamination is small this degradation is particularly severe for the index-coupled laser. Several properties of the index-coupled laser with the HR/AR structure can be improved, however, by introducing the gain-coupling component     

Self-consistent Simulation of self-pulsating two-section gain-coupled DFB lasers

The role of cavity conditions in the dynamics of two-section gain-coupled distributed feedback (DFB) lasers is investigated using a self-consistent model. Self-sustained pulsation (SSP) exists only for devices with strongly coupled DFB gratings. As the coupling strength increases, multiple SSP regimes are developed. The SSP frequency tuning range increases as cavity length decreases. The frequency and modulation index predicted by the model agree well with experimental results. The facet condition of each section is found to affect SSP differently because of the asymmetrical behavior of the modes responsible for SSP.